Details

analyze3.0ms

Algorithm

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
0%	56.2%	43.8%	2
42.1%	14%	43.8%	3
42.1%	14%	43.8%	4
52.7%	3.5%	43.8%	5
56.2%	0%	43.8%	6

sample29.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify112.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (110.0ms)

Iter	Nodes	Cost
0	4949	35
1	4949	35

prune13.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 3.1b

Counts

2 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
0.0b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
586×	`*-un-lft-identity`
340×	`add-sqr-sqrt` `add-cube-cbrt`
123×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
29×	`flip3-+` `flip-+`
27×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
13×	`add-log-exp`
10×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`sum-log`
4×	`pow1` `associate-/l/`
3×	`frac-2neg` `clear-num`
1×	`+-commutative` `associate-+l+`

Counts

4 → 465

Calls

4 calls:

8.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
22.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
36.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
20.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
23.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
18.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify187.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4973	23485
1	4973	23485

prune1.5s

Filtered

288 candidates to 477 candidates (-65.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	467	10	477
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	469	10	479

Merged error: 1.0b

Counts

479 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ alpha beta) (* beta alpha))
0.0b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ beta 3.0)))
2.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

954×	`times-frac`
828×	`*-un-lft-identity`
383×	`add-sqr-sqrt` `add-cube-cbrt`
253×	`distribute-lft-out`
82×	`associate-/l*`
62×	`associate-/r/`
33×	`flip3-+` `flip-+`
31×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/r*`
10×	`cbrt-undiv` `div-exp`
9×	`add-log-exp`
4×	`pow1` `associate-/l/`
3×	`frac-2neg` `clear-num` `sum-log`
1×	`+-commutative` `associate-+l+`

Counts

4 → 524

Calls

4 calls:

6.0ms	(+ (+ alpha beta) (* beta alpha))
20.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
36.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ beta 3.0)))
16.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+ (+ alpha beta) (* beta alpha))
25.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
22.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ beta 3.0)))
12.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify163.0ms

Algorithm

egg-herbie

Counts

536 → 536

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5040	24742

prune1.4s

Filtered

286 candidates to 536 candidates (-87.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	530	6	536
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	537	9	546

Merged error: 1.0b

Counts

546 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ alpha (+ beta (* 1.0 2.0))) (* (/ (+ alpha (+ beta 3.0)) (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0)))))
0.1b	(* (/ (+ alpha (+ beta 3.0)) (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))
0.2b	(/ 1 (* (+ alpha (+ beta (* 1.0 2.0))) (* (/ (+ alpha (+ beta 3.0)) (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))))
2.9b	(/ (+ alpha (+ beta 3.0)) (+ alpha (+ beta (+ (* alpha beta) 1.0))))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

145×	`*-un-lft-identity`
68×	`distribute-lft-out`
54×	`add-exp-log` `times-frac`
36×	`add-sqr-sqrt`
35×	`associate-l`
34×	`frac-times` `add-cbrt-cube`
31×	`add-cube-cbrt`
29×	`flip3-+` `flip-+`
24×	`associate-*r/`
22×	`prod-exp`
21×	`associate-/r/`
17×	`pow1`
14×	`div-exp`
12×	`cbrt-unprod`
11×	`associate-*l/`
8×	`cbrt-undiv` `associate-/l*`
7×	`pow-prod-down`
6×	`associate-/r*`
5×	`distribute-rgt-in` `distribute-lft-in` `associate-r`
4×	`rec-exp` `1-exp` `add-log-exp`
3×	`pow-flip` `div-inv`
2×	`frac-2neg` `clear-num` `*-commutative` `associate-/l/` `unswap-sqr`
1×	`inv-pow`

Counts

4 → 204

Calls

4 calls:

25.0ms	(* (+ alpha (+ beta (* 1.0 2.0))) (* (/ (+ alpha (+ beta 3.0)) (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0)))))
22.0ms	(* (/ (+ alpha (+ beta 3.0)) (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))
26.0ms	(/ 1 (* (+ alpha (+ beta (* 1.0 2.0))) (* (/ (+ alpha (+ beta 3.0)) (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))))
15.0ms	(/ (+ alpha (+ beta 3.0)) (+ alpha (+ beta (+ (* alpha beta) 1.0))))

series101.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (+ alpha (+ beta (* 1.0 2.0))) (* (/ (+ alpha (+ beta 3.0)) (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0)))))
20.0ms	(* (/ (+ alpha (+ beta 3.0)) (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))
23.0ms	(/ 1 (* (+ alpha (+ beta (* 1.0 2.0))) (* (/ (+ alpha (+ beta 3.0)) (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))))
15.0ms	(/ (+ alpha (+ beta 3.0)) (+ alpha (+ beta (+ (* alpha beta) 1.0))))

simplify61.0ms

Algorithm

egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5476	5992

prune534.0ms

Filtered

122 candidates to 216 candidates (-77.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	214	2	216
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	217	8	225

Merged error: 0.1b

Counts

225 → 8

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (+ alpha (+ beta (* 1.0 2.0))) (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))))) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ beta 3.0)))
0.2b	(/ (+ alpha (+ beta (* 1.0 2.0))) (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))))
2.9b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.9b	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

17825×	`times-frac`
16059×	`*-un-lft-identity`
6007×	`add-sqr-sqrt`
6005×	`add-cube-cbrt`
5692×	`distribute-lft-out`
5290×	`sqrt-prod`
823×	`associate-/l*`
286×	`associate-/r/`
258×	`sqrt-div`
152×	`div-inv`
137×	`flip3-+` `flip-+`
20×	`add-exp-log` `add-cbrt-cube`
13×	`associate-/r*`
11×	`cbrt-undiv` `div-exp`
6×	`pow1`
4×	`add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`

Counts

4 → 5033

Calls

4 calls:

234.0ms	(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (+ alpha (+ beta (* 1.0 2.0))) (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))))) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ beta 3.0)))
14.0ms	(/ (+ alpha (+ beta (* 1.0 2.0))) (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))))
7.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))

series142.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (+ alpha (+ beta (* 1.0 2.0))) (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))))) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ beta 3.0)))
84.0ms	(/ (+ alpha (+ beta (* 1.0 2.0))) (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))))
9.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
9.0ms	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))

simplify1.8s

Algorithm

egg-herbie

Counts

5045 → 5045

Iterations

Useful iterations: 0 (211.0ms)

Iter	Nodes	Cost
0	5457	374805

prune15.6s

Filtered

1085 candidates to 5045 candidates (-365.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	5045	0	5045
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	5045	8	5053

Merged error: 0.1b

Counts

5053 → 8

regimes141.0ms

Accuracy

69.8% (1.2b remaining)

Error of 1.3b against oracle of 0.1b and baseline of 4.1b

bsearch20.0ms

Steps

Iters	Range		Point
8	1.7232092867552332e+161	2.0517522251319839e+164	1.7457244029309327e+161

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	66
1	52	66

end0.0ms

sample822.0ms

Algorithm

intervals

Results

541.0ms	8000×	body	80	valid
140.0ms	8000×	pre	80	true

Details

analyze3.0ms

sample29.0ms

simplify112.0ms

prune13.0ms

localize13.0ms

rewrite109.0ms

series64.0ms

simplify187.0ms

prune1.5s

localize14.0ms

rewrite116.0ms

series63.0ms

simplify163.0ms

prune1.4s

localize17.0ms

rewrite100.0ms

series101.0ms

simplify61.0ms

prune534.0ms

localize29.0ms

rewrite1.0s

series142.0ms

simplify1.8s

prune15.6s

regimes141.0ms

bsearch20.0ms

simplify1.0ms

end0.0ms

sample822.0ms

Profiling